2009•Shuxue de shijian yu renshiRequires access
On the Asymptotic Property of k-free D.H.Lehmer Number
Ren Gang-lian
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Abstract
Let p be a prime,for each positive integer a with 1ap-1,it is clear that there exists one and only one integer a-with 1a-p-1 such that aa-≡1(mod p).For any fixed integer k2,let A denote the set of all k-free number in interval ,the main purpose of this paper is to study the asymptotic properties of the mean valueNk(1,p)=∑a∈A2|a+a-+11and give an interesting asymptotic formula for it.